Estimating stellar limb darkening using exoplanet transits

Abstract: The brightness of the stars is not uniform over the surface as it varies depending on the wavelength and the atmosphere that the light propagates. Limb darkening is an optical effect caused by a decrease in brightness of the star towards the edge. Depending on which point on the star is observed, the optical depth reaches different atmospheric media, which results in different intensities of light. In the case of limb darkening, the light gets absorbed more as it is observed in the outer atmosphere and hence, appears darker than the center. The transit method is one of the exoplanet observation methods which measures a transit depth, a drop in stellar flux due to the exoplanet transit. Such a measurement can be utilized to derive a ratio between stellar radius and planetary radius. Hence, the accurate observation of transit depth is essential for the measurement of the planetary radii. The limb darkening can alter the profile of the transit light curve by making the transit depth deeper, which then affects the measurement of the planetary radii. Several models of limb darkening have been established and improved over the past years. The power-2 limb darkening law is one of the examples, and it provides a good estimation of limb darkening. The primary goal of this Bachelor’s project is to estimate limb darkening by using the light curves observed by one of the ongoing space missions, CHaracterising ExOPlanet Satellite (CHEOPS), and to compare them to the theoretical values calculated with the power-2 limb darkening law. Throughout this project, the light curves of a target, WASP-8b, are analyzed using a Python package, PYCHEOPS. The observational value of limb darkening parameters h1 and h2 are calculated from the analysis of two light curves and compared to the theoretical values listed in Borsato et al. (2021). I also investigated how an increase in the number of analyzed light curves can affect the derived limb darkening parameters. From the analysis of two light curves, I constrained the h1 parameter to h1 = 0.70 ± 0.03 while for the h2 parameter, I only managed to calculate the 95% percentile of h2 = [0.125, 0.708]. For the h1 parameter, the observational value shows an agreement within 1-σ with the theoretical one. For the h2 parameter, the theoretical value lies in the 95% percentile range. When the number of light curves is doubled, the h1 parameter got more constrained with the value of h1 = 0.71 ± 0.01. The h2 parameter, on the other hand, remained unconstrained such that I could only calculate the 95% percentile of h2 = [0.093, 0.679]. Nevertheless, I found a statistical improvement of the observational values and fitted models where a decrease in reduced chi-square value and two times lower BIC are obtained from doubling the number of analyzed light curves. The results and statistical analysis indicate that the limb darkening can be estimated from the CHEOPS light curves using the power-2 limb darkening law.